Loop cut and slide didn't complete the loop
When a loop cut doesn't complete, it is usually because it hits a triangular face.

Before you did the loop cut, you have a misplaced quadrilateral. On the corner where the cut ends, there is an extra edge. If you move to the bottom corner of the object where the line is, there are two extra vertices. 

The image below has the vertices highlighted.



Delete these vertices and then try and complete the loop cut.

You have to ensure that no extra faces like in your mesh exist. If a loop cut fails, your mesh will almost always have an error like this or a triangular face.

Good luck with your project and I hope I helped,

BFB